need to know how to write C programs under linux which can open connection, disconnect, transfer data trough RS232 port between 2 linux box.

Also need to know how to view status of a serial port(if a connection is established), and if possible also control speed, timeout

Specifically need to know after 2 computer is linked using a serial port, when the plug is being pulled.

Try here or here.

Since serial lines are connectionless, you can only detect this condition if you are either transmitting something continuously or agree on DTR always being up by the IFD and detetct it going down.
In serial programming, you always have to poll or select for conditions (status lines, bytes received,...) so you have to implement all the timeout handling yourself. Familiarize yourself well with the 'select()' system call as everything sensible is built around it.
adz has given you serveral links where you will find lots of example code so I won't post extra code here, but feel free to come back here with specific problems.

So long...
bruce